The Ecuador international spoke to media during preparations for the World Cup, where Ecuador are among the South American sides hoping to make an impression in the tournament.
Hincapie, 24, joined Arsenal on loan from Bayer Leverkusen ahead of the 2025/26 season, with the move later converted into a permanent transfer worth €52m.
He quickly established himself as a regular under Mikel Arteta, primarily at left-back, helping Arsenal end a 22-year wait for the Premier League title before adding the Champions League.
"It has been a very special season for me," Hincapie told AS.
"Collectively we achieved important things, and personally I feel I grew a lot. I always try to help the team and keep improving every day."
He said the achievement carried extra weight given the difficulty of breaking into a squad already containing senior centre-backs.
"I'm proud of what we achieved, but I also have a hunger to keep achieving more," Hincapie said.
Hincapie arrived in England having spent four seasons in Germany, where he won the Bundesliga and DFB-Pokal with Bayer Leverkusen.
Adapting to the pace of the Premier League, and to Arteta's demands specifically, was something he addressed head-on from his first day in training.
"The Premier League is a very intense competition, but I arrived with a strong desire to learn," he said.
"Arteta is a very demanding coach and that forces you to improve in every aspect."
He said his early focus was simply on absorbing information from those around him.
"From day one I tried to listen, work hard and adapt to what the team needed."
Hincapie was asked which forwards had impressed him most during his first season facing Premier League opposition on a weekly basis.
"There are many forwards of a very high level in the Premier League," he said.
"But I was struck by coming up against players who combine strength, speed and technical quality. Every week you face different challenges."
The defender, who came through the youth ranks at Independiente del Valle before moving to Europe via Talleres and Leverkusen, was also asked whether this represents the peak of his career so far.
Hincapie suggested there is more to come, despite the scale of what he has already achieved at 24.
"I feel very good and with a lot of confidence, but I think I can still give more," he said.
"I'm only 24 and I want to keep growing. The important thing is to keep my feet on the ground and keep working."
Hincapie's rise mirrors a broader period of success for Ecuadorian players in Europe, with Willian Pacho lifting the Champions League with PSG a year earlier before facing Hincapie's Arsenal in this season's final.
For Ecuador, Hincapie's growing stature in England adds another experienced voice to a squad looking to make a mark at the World Cup, with the defender arriving in the United States on the back of the most successful season of his career.